Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).
If I understand your question, I'd offer that, if you look, for example, at Stoney's plot above, you'll see that Cl = f(alpha) and that that function changes, airfoil to airfoil (2D) and 3d wing to 3d wing (as he shows here for varying aspect ratio) . If you're interested, take a look at, for example, Abbott and Von Doenhoff - it's a classic text on airfoil sections and plots out the cl versus alpha characteristics for many common 2d airfoils. My understanding of the development of most of these plots is that they're empirically derived (i.e., from test). Conceivably, you could "virtually" test 'em now, given CFD but A&vD predates computers as we know them.
And yes, the overall shape dramatically affects the wing characteristics. Consider, for example, cross-flow on swept wings causing higher relative velocities locally or the impact of elliptical planforms on drag and trailing vortex formation.
Speaking, as we were, of aspect ratio, one of the upsides of high AR is low induced drag - and this is related to Stoney's point, imj. Since induced drag is the "dragward" component of lift, and since a high AR wing produces more lift at lower relative AofA, his plot makes good sense. High AR planes tend to climb like demons for this reason - they can make lots of lift without making lots of induced drag - and THAT in turns, is corroborated, as expected, by our own AH Ta-152. The downside? Well, it gives it up in stall sooner too.